Summary 307 Linear Inequalities and Systems of Linear Inequalities in Two Variables Examples Example 1 Graph the solution to the inequality . Solve for y: 2x y 6 4 y 6 2x 4 y 7 2x 4 Graph the related equation, with a dashed line. Shade above the line. y 2x 4, 2x y 6 4 Section 3.5 AxBy 6 C, AxBy 7 C, AxByC, Ax By C. You can use test points to check that you have shaded the correct region. Select an ordered pair from the proposed solution set and substitute the values of x and y in the original inequality. If the test point produces a true statement, then you have shaded the correct region. The union or intersection of two or more linear inequalities is the union or intersection of the solution sets. Example 2 Graph the solution set. x 6 0 and y 7 2 Example 3 Graph the solution set. x 0 or y 2 y x 5 4 3 2 1 4 3 1 3 4 5 21 1 2 3 4 5 5 2 Key Concepts A linear inequality in two variables is an inequality of the form or Graphing a Linear Inequality in Two Variables 1. Solve for y, if possible. 2. Graph the related equation. Draw a dashed line if the inequality is strict, < or >. Otherwise, draw a solid line. 3. Shade above or below the line according to the following convention. • Shade above the line if the inequality is of the form y 7 mx b or y mx b . • Shade below the line if the inequality is of the form y 6 mx b or y mx b. 5 3 21 1 1 y x 5 4 3 21 2 1 543 1 2 3 4 5 1 2 3 4 5 y x 4 4 3 1 2 3 4 5 2 3 4 5 5
miller_intermediate_algebra_4e_ch1_3
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